Connections within the group of differentiated gamma functions and with other function groups

Representations through more general functions

The differentiated gamma functions , , , and are particular cases of the more general hypergeometric and Meijer G functions. Although the arguments of these functions do not depend on the variable , it is included in their parameters.

For example, , , , and can be represented through generalized hypergeometric functions by the following formulas:

The aforementioned general formulas can be rewritten using the classical Meijer G functions as follows:

Representations through related equivalent functions

The differentiated gamma functions , , , and can be represented through derivatives of the gamma function :

The differentiated gamma functions , , , and can also be represented through derivatives of the logarithm of the gamma function :

The functions and are intimately related to the Hurwitz zeta function and the Bernoulli polynomials and numbers , by the formulas:

Representations through other differentiated gamma functions

The differentiated gamma functions , , , and are interconnected through the following formulas: